With the advances in automation technologies, data science, process modeling and process control, industries worldwide are at the precipice of what is described as the fourth industrial revolution (Industry 4.0). This term was coined in 2011 by the German federal government to define their strategy related to high tech industry , specifically multidisciplinary sciences involving physics-based process modeling, data science and machine learning, cyber-physical systems, and cloud computing coming together to drive operational excellence and support sustainable manufacturing. The boundaries between Information Technologies (I.T.) and Operation Technologies (O.T.) are quickly dissolving and the opportunities for taking lab-scale manufacturing science research to plant and enterprise wide deployment are better than ever before. There are still questions to be answered, such as those related to the future of manufacturing research and those related to meeting such demands with a highly skilled workforce. Furthermore, in this new environment it is important to understand how process modeling, monitoring, and control technologies will be transformed. The aim of the paper is to provide state-of-the-art review of Smart Manufacturing and Industry 4.0 within scope of process monitoring, modeling and control. This will be accomplished by giving comprehensive background review and discussing application of smart manufacturing framework to conventional (machining) and advanced (additive) manufacturing process case studies. By focusing on process modeling, monitoring, analytics, and control within the larger vision of Industry 4.0, this paper will provide a directed look at the efforts in these areas, and identify future research directions that would accelerate the pace of implementation in advanced manufacturing industry.